In this effort, we propose a new fractional differential operator in the open unit disk. The is an extension of Atangana-Baleanu without singular kernel. We suggest it for normalized class analytic functions By employing extended operator, study time-2-D space heat equation and optimizing its solution by chaotic function.

One-dimensional maps showing chaotic intermittency with discontinuous reinjection probability density functions are studied. For these maps, the mechanism possesses two different processes. The M function methodology is applied to analyze complete and determine function. In M(x) continuous non-differentiable. Theoretical equations found for Finally, theoretical results compared numerical data f...

in the paper a model to predict the concentrations of particulate matter pm10, pm2.5, so2, no, co and o3 for a chosen number of hours forward is proposed. the method requires historical data for a large number of points in time, particularly weather forecast data, actual weather data and pollution data. the idea is that by matching forecast data with similar forecast data in the historical data...

Both the stochastic chaotic simulated annealing and the deterministic chaotic simulated annealing are used to restore gray level images degraded by a known shift-invariant blur function and additive noise. The neural networks are modeled to represent the image whose gray level function is the simple sum of the neuron state variables. The restoration consists of two stages: parameter estimation ...

Analysis of nonlinear autonomous systems has been a popular field of study in recent decades. As an interesting nonlinear behavior, chaotic dynamics has been intensively investigated since Lorenz discovered the first physical evidence of chaos in his famous equations. Although many chaotic systems have been ever reported in the literature, a systematic and qualitative approach for chaos generat...

In this paper, in order to show some interesting phenomena of three dimensional autonomous ordinary differential equations, the chaotic behavior as a function of a variable control parameter, has been studied. The complex dynamical behaviors of the system are further investigated by means of eigenvalue structures and various attractors. The chaotic system examined in MATLAB 2010. The Oscillator...

Controlling chaos has become a challenging topic in nonlinear dynamics. It has been studied in many scientific and engineering fields such as physics, chemistry, electrical circuit, etc., and several extension and applications of the original OGY control method [1] have been reported [2–6]. Chua’s circuit is known as an electrical circuit and having the ability of generating chaos [7]. Recent r...

In this paper, a generalized synchronization scheme, which is called function synchronization, for chaotic systems is studied. Based on Lyapunov method and active control method, we design the synchronization controller for the system such that the error dynamics between master and slave chaotic systems is asymptotically stable. For verification of our theory, computer and circuit simulations f...